It is important to stress that the collision phase shifts are far-field effects. Mathematically they are artefacts of the asymptotic representation of the exact two-soliton solution of the KdV equation in the form of a sum of two individual solitons: \(u_2(x,t; \eta _1, \eta _2) \simeq u_s(x+\Delta _{12},t; \eta _1)+u_s(x+\Delta _{21},t; \eta _2)\) , which
is only valid if solitons are sufficiently separated (the long-time asymptotics). The interaction of solitons is a complex nonlinear process [1]} and the resulting wave field in the interaction region cannot be represented as a superposition of the phase-shifted one-soliton solutions.
